The document discusses various methods for demand forecasting, including qualitative and quantitative approaches. Qualitative methods involve expert judgment through individual specialists, group consensus, or the Delphi method. Quantitative methods include causal models using regression analysis and time series analysis. Simple time series models discussed are the projection method, simple moving average, weighted moving average, and basic exponential smoothing. Accuracy of forecasts is also addressed through measures like average error, bias, and mean absolute deviation. The document provides an example application of these time series models to a sample demand data set.

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 9, Issue 12, December 2018, pp. 163–173, Article ID: IJCIET_09_12_020
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=12
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
©IAEME Publication Scopus Indexed
MODELING OF THE DEMAND FORECASTING
Mikhail Samuilovich Gasparian, Mikhail Vladimirovich Karmanov,
Irina Anatolievna Kiseleva, Vladimir Ivanovich Kuznetsov,
Natalia Alekseevna Sadovnikova
Plekhanov Russian University of Economics, 117997,
Russian Federation, Moscow, Stremyanny lane, 36
ABSTRACT
An attempt to forecast demand and build forecasting models is made in the article.
The modern business is conducted in the context of fierce competition. Adequate
decisions require deep, comprehensive assessment of the situation and a reliable
forecast of developments. Proven methods of forecasting by extrapolation of the
previous results to the future are poorly suited for qualitative changes in the economy,
especially in a complex, dynamic, and uncertain environment. A company that has
managed to forecast the situation correctly earns additional profit in comparison with
the one that abstained from forecasting. A firm that made the wrong forecast loses the
most. The simplest forecast is to extrapolate the current situation to the future. This
technique may be well suited for a stable and clear situation, but it begins to fail in a
dynamic and uncertain environment, as well as in the context of structural
adjustments.
The article provides an analysis of the qualitative and quantitative methods of
the demand forecasting. More complex techniques of time series include factors of
trends, seasonal patterns, and economic cycles. Models of simple time series and
the Holt's model of exponential smoothing are reviewed, and a lot of attention is paid
to the deseasonalized demand.
Key words: model, demand, forecasting, time series models
Cite this Article: Mikhail Samuilovich Gasparian, Mikhail Vladimirovich Karmanov,
Irina Anatolievna Kiseleva, Vladimir Ivanovich Kuznetsov, Natalia Alekseevna
Sadovnikova, Modeling of the Demand Forecasting, International Journal of Civil
Engineering and Technology (IJCIET) 9(12), 2018, pp. 163–173.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=12
1. INTRODUCTION
Key parts of the supply chain planning are demand planning and the associated process of
demand forecasting. The supply chain planning largely begins with forecasting [1].
Since most production systems cannot instantly respond to consumer demand, some
assessment or the forecast of future demand is needed to develop efficient operational plans.
The process and labor intensity are established on the basis of future demand forecasts.

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Capacity planning and decision making for facilities will be mainly based on long-term,
cumulative forecasts [2].
However, forecasts are also required for planning the appropriate levels of inventory,
which generally requires short-term forecasts at a disaggregated level, since specific
components, parts and finite elements must be stocked up for the immediate consumer
demand.
Forecasts influence most functional areas of a firm and are a starting point for making
decisions about the allocation of resources. For instance, production should be daily planned
to meet customer orders, while the procurement department should know how to arrange
deliveries with the production schedule. The finance department needs forecasts to ensure an
adequate level of investment in installation, equipment, and inventory so that budgets can be
planned to better manage the business. The marketing function serves to allocate resources for
various product groups and marketing campaigns [3]. Forecasts also define labor
requirements of a firm so that the HR function can make appropriate hiring and training
decisions when demand is expected to grow.
2. METHODS OF THE DEMAND FORECASTING
Forecasting is based on a combination of qualitative and quantitative indicators [4-6].
Qualitative method. A person’s judgment can be recorded in several ways. Three common
approaches include the individual market specialist, group consensus, and the Delphi method.
They are sometimes referred to as expert methods, since they require people with some
knowledge of products and markets to develop forward-looking estimates for planning needs.
Individual market specialists can be hired to track industry trends, perhaps even
geographically, and work with retailers to assess future demand for products. However,
individuals have preconceptions they may be unaware of, and there is a limit to how much
information one person can get. A group of experts should be used to overcome this, although
it may be much more expensive.
The group consensus unites experts from various fields to reach a common opinion on
future forecasts for a product or group of products. As a rule, the forecasts of the group unite
different factions of the company.
The group is trying to ensure that overly zealous managers do not overestimate the results
of the forecast in order to really meet the firm's expectations of growth. The group can also
make sure that someone is playing the role of a conservative, because this person considers it
less dangerous to underestimate the forecast. However, there are some pitfalls in using a
group consensus. When people from different ranks in a firm get together, this can make staff
at some point agree with senior managers in the group. This wins in reaching a general
agreement and can be a real problem for some.
One way to overcome this problem is to reach an anonymous consensus using the Delphi
method. It requires one person to administer and coordinate the process and interview team
members (respondents) through a series of consecutive questionnaires. At the same time, team
members should be people with experience in a field of interest for the forecast, and an
administrator should only have some knowledge of how to coordinate efforts without unduly
influencing the results.
Questionnaires that are provided to team members include not only demand estimates.
They aim to determine how each participant reaches this estimate. Once everyone has
returned the questionnaires, the administrator should summarize the results and send the final
report to all respondents, but with an indication of who made the forecast hidden from the
team. This process continues until participants reach a certain consensus on the forecast. Of

3. Mikhail Samuilovich Gasparian, Mikhail Vladimirovich Karmanov, Irina Anatolievna Kiseleva,
Vladimir Ivanovich Kuznetsov, Natalia Alekseevna Sadovnikova
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course, this method can be both time consuming and quite expensive to administer, but at the
same time, it can result in good forecasts and, moreover, make an important contribution to
the process over time. Three rounds are a good compromise between the forecast quality, cost,
and efforts.
Quantitative method. Quantitative analysis usually involves two approaches: causal
models and time series methods. Causal models establish a quantitative relationship between
some observable or given variable (for example, advertising costs) and the demand for a
certain product. Time series analysis involves analyzing the historical demand for a product to
forecast future demand.
The most common types of causal models are regression analysis and econometric
models. Although regression models can be involved, a simple linear regression is often used,
where a straight line Y = mX + b is used to describe the relationship between the dependent
variable Y and the independent variable X. A line is placed through a set of points in such a
way that the square distance from the line is minimized – as such, the “smallest square” is
appropriate. Econometric models typically represent some form of a multidimensional
regression model, where independent variables are such factors as disposable income and
industrial output from the economy.
Mathematical details of the regression are not reviewed in this article. There are several
different time series models, most of which work on the basis of the assumption that historical
demand can be "smoothed out" by averaging. A simple time series analysis includes models
such as weighted moving average and basic exponential smoothing. More complex time series
methods include factors of trends, seasonal patterns, and economic cycles. The focus will later
be put on these time series models.
3. SIMPLE TIME SERIES MODELS
Some of the most popular forecasting methods, especially in software, are commonly referred
to as time series models. These models use past data to forecast future demand [7-9]. This
type of forecasting method is especially important for items that are constantly streamlined,
because these methods can be to a great extent “automated” in computer information systems.
The models assume that each observed demand data point consists of some systematic
component and some random component. The time series model is intended to predict a
systematic component, but not a random component. The idea is similar to the logic of quality
control diagrams – that one should not try to respond to the variability of the process if the
latter is within control. Responding (or changing the forecast model) due to random errors is
likely to lead to an increase in errors in future forecasts. It is necessary to try and forecast the
range or variation of this random error. Models can be designed for almost any type of
systematic change in demand, but there is a real danger in predicting the random component.
Projection
The simplest time series method simply forecasts future demand based on demand from the
last period. The forecast for the next period is just a projection of this period t of
demand
Although this method is easy to use, it does not use the data that are easily accessible to
most managers. As such, using more historical data should improve the forecast. Past demand
averages may be more useful [10, 11].
Simple moving average (SMA)

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SMA forecast allows for a better use of historical data about demand than the demand for
the past period. The moving average uses the last n demand periods as a forecast for the future
demand periods:
This forecast model is most useful when the level of demand is fairly constant over time.
Then the model makes simple adjustments to this average level instead of assuming that the
level is always constant. Its advantage over the projection model is that the forecast will not
tend to fluctuate when averaged. The average value of the previous n periods can be
considered as an estimate of the average level of demand for period t. As such, level Lt can
be determined as follows:
and, consequently, forecast is only the latest estimate of the level of demand.
Weighted moving average (WMA)
One of the disadvantages of SMA is the equal weight of the data. For example, a 5-period
moving average weighs each of the last 5 demand requests equally – each of them has 20%
impact on the forecast. This contradicts the fact that the most recent data are the most
relevant. As such, WMA allows to pay more attention to the most recent data. This forecast is
as follows:
where is the weight applied to the demand incurred during period t, is the weight
defined for period t-1, etc. It was intuitively expected that the most recent demand data should
be weighed more strongly than older data; therefore, as a rule, one would expect that the
weights would correspond to the following ratio:
Basic exponential smoothing (BES)
The WMA properties will be good in the case where the weights do not only decrease as older
data are used, but where differences between weights are "smooth". Obviously, the weight of
the most recent data should be the largest. Then weights should be gradually reduced, in
accordance with the past periods. The exponentially decreasing weights of the main
exponential smoothing forecast are consistent with this calculation. The prediction equation is
given as follows:
( )
where α is the smoothing parameter between 0 and 1. To show that this forecast is actually
a weighted average forecast, let us consider the algebraic extension of the model.
Since
( )
( )[ ( ) ]
( ) ( ) ( ) ⟦( ) ( )]
This can also be extended
( )

5. Mikhail Samuilovich Gasparian, Mikhail Vladimirovich Karmanov, Irina Anatolievna Kiseleva,
Vladimir Ivanovich Kuznetsov, Natalia Alekseevna Sadovnikova
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( ) ( ) [ ( ) ]
( ) ( ) ( )
Continuing this extension, the model can be written as follows:
( ) ( ) ( )
As such, the exponential smoothing model is actually a WMA model with special
weights. These weights are gradually reduced as they are applied to periods farther from the
current period. Calculations help show that these weights add up to 1:
( ) ( ) ( )
Despite the fact that these weights have important properties, there is no need to track
every weight. Moreover, the system working with the model does not need to store historical
data or calculate something based on old data. All it needs is the smoothing factor α, the
demand of the last period, and the forecast of the last period. The advantage of the model is
that all data of the past demand remain in the forecast of the last period. [12, 13].
Example of a simple time series
The models presented above can be illustrated using a simple data set. Data on the demand for
a product for the period from January to August are given in Table 1. The period designation
in the table is the same as indicated in the models.
Table 1 Seasonal estimates and baseline seasonal factors
Month January February March April May June July August
Period t-7 t-6 t-5 t-4 t-3 t-2 t-1 t
Demand 45 60 42 46 52 47 41 48
A firm wants to forecast demand for September (period t + 1). These calculations are
presented below.
1) Simple projection
SMA (using 4 periods)
2) WMA (using 4 periods )
3)
4) BES (с α = 0.2)
To use BES, the firm uses retrospective demand data to test the model. To do this,
forecasts for each period with available demand data should be calculated. Table 2 shows the
forecast for September and the calculations required to obtain this forecast using an
exponential model.
Smoothing occurs in forecasting based on the past data, thus, the future forecasts are
based on good weights. The use of the past data also allows the forecaster to measure forecast
errors based on the model, assuming that it was actually used in the past to make forecasts.

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Table 2 Calculations using the BES method
Month Period Demand 0.2* +0.8* Forecast
January t-7 45 47
February t-6 50 0.2*45+0.8*47 46.6
March t-5 42 0.2*50+0.8*46.6 47.3
April t-4 46 0.2*42+0.8*47.3 46.2
May t-3 52 0.2*46+0.8*46.2 46.2
June t-2 47 0.2*52+0.8*47.3 47.3
July t-1 41 0.2*47+0.8*47.3 47.3
August t 48 0.2*41+0.8*47.3 46
September t-1 0.2*48+0.8*46 46.4
*Assume the January forecast was 47
Forecast accuracy
Since forecasts are erroneous in most cases, the estimation of the forecast inaccuracy can be
just as useful as the forecast of the expected demand. This is why a good forecast should
include an average value and an estimate of how the forecast will vary depending on the
average. This measure helps understand the risk of the forecast and allows to make decisions
that allow for the existing variability. Forecasting involves estimating more than expected
demand – it is also an attempt to estimate uncertainty [14, 15].
Simple average error over n periods is as follows:
∑
In fact, it would be good to know the AEn value, since it indicates how well the forecast
tracks the actual demand. Such a more widespread measure, known as bias, is commonly used
to track this "regular" error and is given as follows:
∑
Managers are interested in forecasts without bias [16, 17]. If there is prejudice, it is likely
that an incorrect functional forecast model is used. Regular bias should, in theory, be
something that can be eliminated by introducing some factor into the model in order to
remove it from the forecast. As such, this simple measure of an error can be one of the most
important ones in determining whether the correct forecasting model is being used.
Mean absolute deviation. The usual average error measurement used in many companies
is known as mean absolute deviation (MAD). It is represented mathematically as follows:
∑| |
where | |is the absolute value of .
Assuming the absolute value of the error conditions, this error measurement reflects
positive and negative deviations between the forecast and actual demand.
Sample forecast error
The data about demand and forecasts presented in Table 2 will be used to illustrate some of
these errors.

7. Mikhail Samuilovich Gasparian, Mikhail Vladimirovich Karmanov, Irina Anatolievna Kiseleva,
Vladimir Ivanovich Kuznetsov, Natalia Alekseevna Sadovnikova
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The demand is compared with the forecast for each period with the resulting errors in
Table 3. This provides the error values Ei for each period t from January to August. The last
two columns of this table indicate the forecast error and the square forecast error for each of
the periods.
Table 3 Value of the error from January to August
Month Demand Forecast Error
January 45 47 2 4
February 50 46.6 -3.4 11.6
March 42 47.3 5.3 27.9
April 46 46.2 0.2 0.1
May 52 46.2 -5.8 33.9
June 47 47.3 0.3 0.1
July 41 47.3 6.3 39.4
August 48 46 -2 3.9
4. EXPONENTIAL SMOOTHING UPDATES – HOLT MODEL
Each period when information becomes available, level, and trend factors can be updated.
This is done through the equations similar to the equations for BES model presented above. In
BES, smoothing parameter α was used to define the extent to which demand information
should be included in the level factor. There are currently two factors: level and trend, and the
second smoothing parameter β is required to define the amount of smoothing that should be
performed according to the trend coefficient. Values for β range between 0 and 1. Below are
updates of the equations for each factor for the case of additive trend:
( )( )
( ) ( )
Managers want to adjust forecasting models for their most popular products. The demand
for one of the products, which has had phenomenal growth since its introduction, is shown in
Table 4. This product has been on the market since January 2017, and the data on demand for
this product are provided for eleven periods through to November 2017. The firm’s analyst
decided to use the Holt model to forecast future demand and, in particular, to obtain a demand
estimate for December 2017. Since the model assumes an additive trend, a straight line may
be suitable for the data to estimate the initial level factor (interception) and the initial trend
coefficient (line slope). Linear regression forms the following Table 4:
Table 4 Monthly demand
Period Month Demand
1 January 1,404
2 February 1,506
3 March 1,521
4 April 1,658
5 May 1,716
6 June 1,805
7 July 1,919
8 August 1,980
9 September 2,077
10 October 2,220
11 November 2,264
12 December

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Intersection of monthly demand: 1,297 Slope: 87.9
These two terms then become estimates L and T for period 0 (demand was regressed
against periods from 1 to 11) as follows:
= 1297 = 87.9
With the use of the forecast equation, the forecast for period 1 is as follows:
To continue, the firm now observes the first period of demand, = 1,404. This
information can be used to update the levels and trend factors to make them current as of
period 1. Let us choose a smoothing parameter α = 0.2 for the factor coefficient.
( )( )
( )( ) ( )( )
It is similar with the smoothing parameter β = 0.3 for the trend coefficient:
( ) ( )
( ) ( ) ) ( )
Now a forecast for period 2 can be made.
Other calculations are shown in Table 5, including the forecast for the period of 12
December 2017. The table also contains errors calculated using a model for forecasting past
data. Most importantly, it can be noted that these errors are absent. As such, there is no
regular bias that would indicate the use of the wrong model.
Table 5 Forecasting the demand value using the Holt model
Period Month Demand Level Trend Forecast Error
0 1,297 87.9
1 January 1,404 1,388.7 89 1,384.9 -19.1
2 February 1,506 1,483.4 90.7 1,477.8 -28.2
3 March 1,521 1,563.5 87.6 1,574.2 53.2
4 April 1,658 1,652.5 88 1,651.1 -6.9
5 May 1,716 1,735.5 86.5 1,740.4 24.4
6 June 1,805 1,818.6 85.5 1,822 17
7 July 1,919 1,907.1 86.4 1,904.1 -14.9
8 August 1,980 1,990.8 85.6 1,993.5 13.5
9 September 2,077 2,076.5 85.6 2,076.3 -0.7
10 October 2,220 2,173.7 89.1 2,162.1 -57.9
11 November 2,264 2,263 89.2 2,262.7 -1.3
12 December 2,352.1
5. DESEASONALIZED DEMAND
Data deseasonalization requires the two following steps:
1. Search for average seasonal demand for the full set of seasons for all available data.
2. Ensuring that averages are centered in the appropriate period.
According to the data on demand, seasons can be made from quarters, months, 4-week
periods, weeks, and any other periods where such a picture could be observed. For example, if
quarters make up seasons, one can find average quarterly demand using average values for
every four quarters in a row. Using data from Table 6, the average quarterly demand for the
first year is as follows:

9. Mikhail Samuilovich Gasparian, Mikhail Vladimirovich Karmanov, Irina Anatolievna Kiseleva,
Vladimir Ivanovich Kuznetsov, Natalia Alekseevna Sadovnikova
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Since this is the average value for the first four periods, this average demand value is
focused on period 2.5, which is an average demand index. This can be seen in Table 6, where
the first set of dark diagonal lines shows 111.5 as averaging according to demand data from
98 to 133. The average value of 113.5 is found in a similar way using the average value for
four consecutive periods starting from period 2.
=113.8
Table 6 Deseasonalization of demand
Deseasonalization
Period Quarter Demand Initial Centered
1 Q1 2014 98
2 Q2 2014 106 111.5
3 Q3 2014 109 113.8 112.8
4 Q4 2014 133 116.3 115
5 Q1 2015 107 119.3 117.8
6 Q2 2015 116 122.5 120.8
7 Q3 2015 121 127.5 125
8 Q4 2015 146 131 129.3
9 Q1 2016 127 134.6 132.9
10 Q2 2016 130 138 136.4
11 Q3 2016 136 141 139.6
12 Q4 2016 159 144.3 142.6
13 Q1 2017 139 148.5 146.4
14 Q2 2017 143 153 150.8
15 Q3 2017 153
16 Q4 2017 177
To make the deseasonalized demand focus on each period rather than between them, each
pair of conditionally focused averages above and below each period must be averaged to get
an estimate for a certain period rather than between periods.
This centered average indicator of the average demand is shown in the last column of
Table 6, where the set of bright lines indicates the result of the average value of two numbers:
111.5 and 113.8. It must be noted that this procedure of the demand deseasonalization is
suitable for seasonal situations when the number of seasons is uniform. An even number of
seasons requires to center the deseasonalized data. If the number of seasons is odd, as in the
case when the data were broken into thirteen four-week seasons, then when all seasons are
averaged, the average value will occur in the middle period, and there would have been no
reason to center the average.
6. CONCLUSIONS
Forecasts are erroneous in most cases, but some of them are "more erroneous" than others.
Forecasting the demand for innovative products and fashion products is usually more difficult
than forecasting the demand for more "marketable" products that are sold daily. Aggregate
forecasts for a group of similar products are usually more accurate than individual forecasts

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for individual products in a group. Finally, the longer the forecast in the future is, the less
reliable it is.
The commodity-like products that are sold daily, on the other hand, are much more
suitable for quantitative models and require little judgment to forecast demand [18, 19].
However, when knowledge of certain events makes one think that future demand may not
track historical trends, one can view some judgments in order to introduce adjustments to the
models using the past data. In this case, a strong dependence on the past data with the
adjustments based on expert estimates should be used for forecasting.
Studies reveal that simple statistical models work well for some everyday commodity
items. However, some managers believe that the forecasts should be made perfect to solve
most of the problems with the supply chain. There are cases when management contribution is
required, but there comes a moment when it is better to understand inaccuracy in the forecast
and plan, respectively. Once a good forecasting process has been implemented (procedures,
methods, models, and management supervision), the continuous improvement is less
significant and may even harm the forecasting process.
Since forecasts are never accurate, two common solutions are often offered to "correct"
the forecast errors [20, 21].
The first is to reduce the execution time in order to respond to changes more quickly. This
is a good partial solution, but reducing the execution time is not always easy and often
expensive. Besides, reducing the execution time in many cases simply transfers problems
from one part of the supply chain to another.
The second is to "make an order" so that the inventory is not produced before demand.
This solution is also good, but, like reducing the execution time, it tends to shift demand to
the next level of the supply chain.
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